Regarding the taper, I am sure we don't want to reduce the spacing over a long enough distance to reduce the impedance below the HDMI tolerance: differential = 100 +/-15% Ohm = [85,115] Ohm, single-ended = 55 +/15% Ohm = [42.5,57.5] Ohm.
What does PADS report for the impedance of our HDMI differential traces on the current or a recent layout?
(We opened up the clearance to 15mil around the differential pairs in order to try to keep the impedance up.) If the impedance is too low, we may need to forgo the taper altogether and just live with the small discontinuities caused by a few vias and component lands that are significantly closer.